What is the time complexity of Find the Substring With Maximum Cost?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Find the Substring With Maximum Cost?

This problem uses Array, Hash Table, String, Dynamic Programming. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Find the Substring With Maximum Cost?

Insight 1: The problem can be solved using a modified Kadane's algorithm, where we track the maximum cost ending at each position. Insight 2: A crucial aspect is efficiently determining the value of each character in the string 's' based on whether it's present in 'chars' or not.

Which companies ask LeetCode 2606. Find the Substring With Maximum Cost in interviews?

This problem is frequently asked at josh technology.

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Find the Substring With Maximum Cost - LeetCode 2606 Solution

Find the Substring With Maximum Cost - Complete Solution Guide

Find the Substring With Maximum Cost is LeetCode problem 2606, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given a string s , a string chars of distinct characters and an integer array vals of the same length as chars . The cost of the substring is the sum of the values of each character in the substring. The cost of an empty string is considered 0 . The value of the character is defined in the following way: If the character is not in the string chars , then its value is its corresponding position (1-indexed) in the alphabet. For example, the value of 'a' is 1 , the value of 'b' is 2 , and s

Detailed Explanation

The problem asks us to find the maximum cost substring within a given string 's'. The cost of a substring is the sum of the values of its characters. The value of each character is determined as follows: If the character is present in the string 'chars', its value is taken from the corresponding 'vals' array. Otherwise, the character's value is its position in the alphabet (a=1, b=2, ..., z=26). The task is to find the substring of 's' that yields the highest possible cost.

Solution Approach

The solution utilizes a dynamic programming approach similar to Kadane's algorithm. First, we create a map (or array in C) to store the values of all characters. Initially, we assign the values 1 to 26 to 'a' to 'z', respectively. Then, we update the values for the characters present in 'chars' with their corresponding values from the 'vals' array. After setting up the character value map, we iterate through the input string 's', calculating the 'current_cost' as we go. The 'max_cost' is updated at each step. If the 'current_cost' becomes negative, it means that including the current substring reduces the overall cost, so we reset it to 0 to start a new substring.

Step-by-Step Algorithm

Step 1: Create a data structure (hash map or array) to store the values for all lowercase English letters (a-z). Initially, assign values 1 to 26 to 'a' to 'z', respectively.
Step 2: Iterate through the 'chars' and 'vals' arrays, updating the character values in the created data structure with the values from 'vals'.
Step 3: Initialize 'max_cost' and 'current_cost' to 0.
Step 4: Iterate through the input string 's'. For each character:
Step 5: Add the value of the current character (obtained from the character value map) to 'current_cost'.
Step 6: Update 'max_cost' with the maximum of 'max_cost' and 'current_cost'.
Step 7: If 'current_cost' is negative, reset it to 0.
Step 8: Return 'max_cost'.

Key Insights

Insight 1: The problem can be solved using a modified Kadane's algorithm, where we track the maximum cost ending at each position.
Insight 2: A crucial aspect is efficiently determining the value of each character in the string 's' based on whether it's present in 'chars' or not.
Insight 3: Resetting the current cost to 0 when it becomes negative is essential for finding the maximum cost substring, as a negative cost substring will always reduce the total cost.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Hash Table, String, Dynamic Programming.

Companies

Asked at: josh technology.

Find the Substring With Maximum Cost | LeetCode 2606

Medium

Array Hash Table String Dynamic Programming

Time: O(n)Space: O(1)

Solution Code

Available in:

import java.util.HashMap;
import java.util.Map;

class Solution {
    public int maximumCostSubstring(String s, String chars, int[] vals) {
        Map<Character, Integer> charValues = new HashMap<>();
        for (int i = 0; i < 26; i++) {
            charValues.put((char)('a' + i), i + 1);
        }

        for (int i = 0; i < chars.length(); i++) {
            charValues.put(chars.charAt(i), vals[i]);
        }

        int maxCost = 0;
        int currentCost = 0;

        for (char c : s.toCharArray()) {
            currentCost += charValues.get(c);
            maxCost = Math.max(maxCost, currentCost);
            if (currentCost < 0) {
                currentCost = 0;
            }
        }

        return maxCost;
    }
}

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Problem Info

Description

Problem 2606: Find the Substring With Maximum Cost - Detailed explanation and solution approaches.

Topics

Array Hash Table String Dynamic Programming

Companies

josh technology

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2606

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

8 steps

1
Step 1: Create a data structure (hash map or array) to store the values for all lowercase English letters (a-z). Initially, assign values 1 to 26 to 'a' to 'z', respectively.
2
Step 2: Iterate through the 'chars' and 'vals' arrays, updating the character values in the created data structure with the values from 'vals'.
3
Step 3: Initialize 'max_cost' and 'current_cost' to 0.
4
Step 4: Iterate through the input string 's'. For each character:
5
Step 5: Add the value of the current character (obtained from the character value map) to 'current_cost'.
6
Step 6: Update 'max_cost' with the maximum of 'max_cost' and 'current_cost'.
7
Step 7: If 'current_cost' is negative, reset it to 0.
8
Step 8: Return 'max_cost'.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is determined by the single loop that iterates through the input string 's'. The space complexity is constant as the hash map/array's size does not scale with input size.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Brute Force

Calculate the cost of every possible substring and find the maximum among them. Iterate through all possible start and end indices of substrings.

Time: O(n^2), where n is the length of string 's'Space: O(1)

Trade-offs: The brute force approach is simple to understand but highly inefficient for large input strings compared to Kadane's Algorithm.

✨

Key Insights

1Insight 1: The problem can be solved using a modified Kadane's algorithm, where we track the maximum cost ending at each position.
2Insight 2: A crucial aspect is efficiently determining the value of each character in the string 's' based on whether it's present in 'chars' or not.
3Insight 3: Resetting the current cost to 0 when it becomes negative is essential for finding the maximum cost substring, as a negative cost substring will always reduce the total cost.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

Dynamic Programming

Breaking complex problems into smaller subproblems and storing results.

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: The input string 's' is empty. The algorithm correctly returns 0, as the cost of an empty string is defined as 0.
Edge case 2: All characters in 's' have negative values. Kadane's algorithm ensures that the maximum cost substring is 0 in this case.
Edge case 3: 'chars' is an empty string. The algorithm correctly uses the default alphabetical values for all characters in 's'.
Edge case 4: The length of 's' is 1. The algorithm returns the value of that single character correctly.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not resetting 'current_cost' to 0 when it becomes negative. This leads to incorrect calculation of the maximum cost substring because a negative cost will always decrease overall cost.

✗Common mistake 2: Incorrectly calculating the value of a character when it is present in 'chars'. It's essential to use the correct index from the 'vals' array.

✗Common mistake 3: Assuming only characters in chars can have negative values; the default alphabetical values could also result in negative overall cost for some substrings if chars contains all letters up to a certain point, all assigned negative values.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Analyzing stock prices over time. The 's' string could represent a series of daily stock price changes (positive or negative), and the algorithm helps find the period with the maximum profit (maximum cost substring).

🏦Real-world scenario 2: DNA sequence analysis. Finding regions with the highest 'score' (where the score is determined by specific base pair combinations) can be framed as finding the maximum cost substring within a DNA sequence.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Consider multiple approaches before coding. Mentioning alternatives shows breadth of knowledge.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: August 26, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 14

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 7

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Find the Substring With Maximum Cost"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether hash table techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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